Finite Element Method E-Book

Gouri Dhatt

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 406

Veröffentlichungsjahr: 2012

Beschreibung

This book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences. The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus. The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.

Leseprobe

Table of Contents

Introduction

0.1 The finite element method

0.2 Object and organization of the book

0.3 Numerical modeling approach

Bibliography

Conference proceedings

Monographs

Periodicals

CHAPTER 1: Approximations with finite elements

1.0 Introduction

1.1 General remarks

1.2 Geometrical definition of the elements

1.3 Approximation based on a reference element

1.4 Construction of functions N(ξ) and

1.5 Transformation of derivation operators [ZIE 00]

1.6 Computation of functions N, their derivatives and the Jacobian matrix

1.7 Approximation errors on an element

1.8 Example of application: rainfall problem

Bibliography

CHAPTER 2: Various types of elements

2.0 Introduction

2.1 List of the elements presented in this chapter

2.2 One-dimensional elements

2.3 Triangular elements (two dimensions)

2.4 Quadrilateral elements (two dimensions)

2.5 Tetrahedral elements (three dimensions)

2.6 Hexahedric elements (three dimensions)

2.7 Prismatic elements (three dimensions)

2.8 Pyramidal element (three dimensions)

2.9 Other elements

Bibliography

CHAPTER 3: Integral formulation

3.0 Introduction

3.1 Classification of physical systems [CRA 56; COL 66;KRE 88; FAR 82]

3.2 Weighted residual method [FIN 72]

3.3 Integral transformations

3.4 Functionals [MIK 64; MIK 71]

3.5 Discretization of integral forms

3.6 List of PDEs and weak expressions

Bibliography

CHAPTER 4: Matrix presentation of the finite element method

4.0 Introduction

4.1 The finite element method

4.2 Discretized elementary integral forms We

4.3 Techniques for calculating elementary matrices

4.4 Assembly of the global discretized form W

4.5 Technique of assembly

4.6 Properties of global matrices

4.7 Global system of equations

4.8 Example of application: Poisson’s equation

4.9 Some concepts about convergence, stability and error calculation

Bibliography

CHAPTER 5: Numerical Methods

5.0 Introduction

5.1 Numerical integration

5.2 Solving systems of linear equations [CAR 69; BAT 79]

5.3 Solution of nonlinear systems

5.4 Resolution of unsteady systems [BAT 76; CRA 56; CLO 75]

5.5 Methods for calculating the eigenvalues and eigenvectors [BAT 76; CRA 56; WIL 65]

Bibliography

CHAPTER 6: Programming technique

6.0 Introduction

6.1 Functional blocks of a finite element program

6.2 Description of a typical problem

6.3 General programs

6.4 Description of the finite element code

6.5 Library of elementary finite element method programs

6.6 Examples of application

APPENDIX — SPARSE SOLVER

7.0 Introduction

7.1 Methodology of the sparse solver

7.2 Numerical examples

Bibliography

Index

First published 2012 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd 27–37 St George’s Road London SW19 4EU UKwww.iste.co.ukJohn Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USAwww.wiley.com

© ISTE Ltd 2012

The rights of Gouri Dhatt, Gilbert Touzot and Emmanuel Lefrançois to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2012946444

British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-84821-368-5